The Normalizer Conjecture in the Alternative Case

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: alternative ring unit loop normalizer
• 年，卷（期）: 2001,（4）
• 页码范围: 455-462
• 页数: 8页
• 分类号: O1
• 语种: 英文

摘要

Let L be a torsion loop for which the integral loop ring ZL is an alternative, but not associative, ring. Let Nu(L) denote the normalizer of L in the unit loop u(ZL). We show that Nu(L) = Z(u)L, where Z(u) is the center ofu(ZL), and use this fact to show that u(ZL) has central height 1, unless L is a hamiltonian 2-loop.